12n
0743
(K12n
0743
)
A knot diagram
1
Linearized knot diagam
4 10 12 10 1 3 11 4 1 8 7 6
Solving Sequence
7,11
8
3,12
4 6 1 5 10 2 9
c
7
c
11
c
3
c
6
c
12
c
5
c
10
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
24
+ 40u
23
+ ··· + 2b + 42, 11u
24
− 78u
23
+ ··· + 4a + 44, u
25
− 8u
24
+ ··· − 42u + 4i
I
u
2
= h−424456u
7
a
3
− 1015802u
7
a
2
+ ··· − 1966550a − 824409, 5u
7
a
2
− 3u
7
+ ··· + 6a + 5,
u
8
+ u
7
+ 5u
6
+ 4u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 1i
I
u
3
= h−u
12
− 2u
11
− 8u
10
− 13u
9
− 24u
8
− 30u
7
− 31u
6
− 26u
5
− 12u
4
− 3u
3
+ 4u
2
+ b + 2u,
− u
12
− 3u
11
− 10u
10
− 21u
9
− 37u
8
− 54u
7
− 61u
6
− 57u
5
− 38u
4
− 15u
3
+ u
2
+ a + 6u + 2,
u
15
+ 3u
14
+ ··· + u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 72 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−5u
24
+ 40u
23
+ · · · + 2b + 42, 11u
24
− 78u
23
+ · · · + 4a + 44, u
25
−
8u
24
+ · · · − 42u + 4i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−
11
4
u
24
+
39
2
u
23
+ ··· +
153
4
u − 11
5
2
u
24
− 20u
23
+ ··· +
421
2
u − 21
a
12
=
u
u
a
4
=
−
11
4
u
24
+
39
2
u
23
+ ··· −
183
4
u − 1
5
2
u
24
− 20u
23
+ ··· +
253
2
u − 11
a
6
=
3
2
u
24
−
25
2
u
23
+ ··· +
297
2
u −
31
2
3
2
u
24
− 11u
23
+ ··· − 132u
2
+
33
2
u
a
1
=
−
15
4
u
24
+
57
2
u
23
+ ··· −
815
4
u + 19
3
2
u
24
− 13u
23
+ ··· +
477
2
u − 27
a
5
=
11
4
u
24
−
39
2
u
23
+ ··· +
247
4
u − 1
−
5
2
u
24
+ 20u
23
+ ··· −
285
2
u + 13
a
10
=
−u
u
3
+ u
a
2
=
−
3
4
u
24
+
9
2
u
23
+ ··· +
401
4
u − 17
5
2
u
24
− 19u
23
+ ··· +
229
2
u − 11
a
9
=
3
2
u
24
−
23
2
u
23
+ ··· +
163
2
u −
15
2
−
1
2
u
24
+ 4u
23
+ ··· −
113
2
u + 6
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
24
− 7u
23
+ 36u
22
− 132u
21
+ 395u
20
− 976u
19
+ 2048u
18
−
3675u
17
+ 5648u
16
− 7378u
15
+ 7999u
14
− 6778u
13
+ 3633u
12
+ 552u
11
− 4251u
10
+
6027u
9
− 5445u
8
+ 3234u
7
− 776u
6
− 810u
5
+ 1221u
4
− 894u
3
+ 414u
2
− 118u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 18u
24
+ ··· + 200u − 192
c
2
, c
8
u
25
+ u
24
+ ··· + 49u − 85
c
3
, c
6
u
25
− 4u
23
+ ··· + 7u − 1
c
4
, c
9
u
25
+ 17u
23
+ ··· + u − 1
c
5
, c
12
u
25
+ 16u
24
+ ··· − 2816u − 256
c
7
, c
10
, c
11
u
25
+ 8u
24
+ ··· − 42u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 28y
24
+ ··· + 395968y −36864
c
2
, c
8
y
25
+ 23y
24
+ ··· − 26159y −7225
c
3
, c
6
y
25
− 8y
24
+ ··· + 71y −1
c
4
, c
9
y
25
+ 34y
24
+ ··· − 11y −1
c
5
, c
12
y
25
+ 14y
24
+ ··· + 393216y −65536
c
7
, c
10
, c
11
y
25
+ 26y
24
+ ··· − 164y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921555 + 0.389569I
a = −0.228724 + 0.336449I
b = 0.714884 + 0.733561I
−3.72259 − 5.55262I 1.00846 + 5.11814I
u = 0.921555 − 0.389569I
a = −0.228724 − 0.336449I
b = 0.714884 − 0.733561I
−3.72259 + 5.55262I 1.00846 − 5.11814I
u = 0.754292 + 0.675553I
a = 0.935089 + 0.407093I
b = 1.02266 − 1.00894I
−4.63523 + 10.99550I 0.61931 − 7.61444I
u = 0.754292 − 0.675553I
a = 0.935089 − 0.407093I
b = 1.02266 + 1.00894I
−4.63523 − 10.99550I 0.61931 + 7.61444I
u = 0.911256 + 0.682747I
a = −0.409833 − 0.368341I
b = −0.863640 + 0.290917I
−8.28803 + 3.15505I −4.81935 − 5.19613I
u = 0.911256 − 0.682747I
a = −0.409833 + 0.368341I
b = −0.863640 − 0.290917I
−8.28803 − 3.15505I −4.81935 + 5.19613I
u = −0.781714
a = −0.294872
b = −0.129373
1.14840 15.4840
u = 0.160604 + 0.683864I
a = 0.447358 − 1.171790I
b = −0.556568 − 0.593706I
2.37371 − 1.53413I 1.38623 + 4.98201I
u = 0.160604 − 0.683864I
a = 0.447358 + 1.171790I
b = −0.556568 + 0.593706I
2.37371 + 1.53413I 1.38623 − 4.98201I
u = −0.03035 + 1.46200I
a = −0.958194 − 0.059340I
b = −0.676699 + 0.397676I
−4.72338 − 2.11817I 0.56869 + 3.89890I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03035 − 1.46200I
a = −0.958194 + 0.059340I
b = −0.676699 − 0.397676I
−4.72338 + 2.11817I 0.56869 − 3.89890I
u = 0.05488 + 1.48295I
a = 1.56598 + 0.02201I
b = 1.097930 − 0.735677I
−7.25788 + 1.53536I −4.26963 − 0.95697I
u = 0.05488 − 1.48295I
a = 1.56598 − 0.02201I
b = 1.097930 + 0.735677I
−7.25788 − 1.53536I −4.26963 + 0.95697I
u = 0.09014 + 1.48837I
a = −1.94282 + 0.27279I
b = −1.22851 + 1.14146I
−2.73659 + 5.21328I −0.241059 − 0.933200I
u = 0.09014 − 1.48837I
a = −1.94282 − 0.27279I
b = −1.22851 − 1.14146I
−2.73659 − 5.21328I −0.241059 + 0.933200I
u = 0.365223 + 0.343863I
a = −0.89848 − 1.63604I
b = −0.883594 + 0.949370I
3.39737 + 3.68728I −2.66049 − 0.54617I
u = 0.365223 − 0.343863I
a = −0.89848 + 1.63604I
b = −0.883594 − 0.949370I
3.39737 − 3.68728I −2.66049 + 0.54617I
u = 0.24700 + 1.59114I
a = 1.88690 − 0.20760I
b = 1.32178 − 1.12604I
−12.1188 + 14.7263I −1.91172 − 6.80862I
u = 0.24700 − 1.59114I
a = 1.88690 + 0.20760I
b = 1.32178 + 1.12604I
−12.1188 − 14.7263I −1.91172 + 6.80862I
u = 0.203322 + 0.330620I
a = 0.46453 + 1.62148I
b = 0.687664 − 0.321221I
−1.185540 + 0.658151I −5.01541 − 1.91955I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203322 − 0.330620I
a = 0.46453 − 1.62148I
b = 0.687664 + 0.321221I
−1.185540 − 0.658151I −5.01541 + 1.91955I
u = 0.27991 + 1.60858I
a = −1.43237 − 0.19401I
b = −1.200770 + 0.592773I
−15.8446 + 7.4948I −4.78217 − 4.06320I
u = 0.27991 − 1.60858I
a = −1.43237 + 0.19401I
b = −1.200770 − 0.592773I
−15.8446 − 7.4948I −4.78217 + 4.06320I
u = 0.43302 + 1.62881I
a = 0.467991 + 0.457927I
b = 0.629543 + 0.114371I
−9.98504 − 0.27176I −10.12478 + 1.72289I
u = 0.43302 − 1.62881I
a = 0.467991 − 0.457927I
b = 0.629543 − 0.114371I
−9.98504 + 0.27176I −10.12478 − 1.72289I
7
II. I
u
2
= h−4.24 × 10
5
a
3
u
7
− 1.02 × 10
6
a
2
u
7
+ · · · − 1.97 × 10
6
a − 8.24 ×
10
5
, 5u
7
a
2
− 3u
7
+ · · · + 6a + 5, u
8
+ u
7
+ 5u
6
+ 4u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
a
0.214472a
3
u
7
+ 0.513271a
2
u
7
+ ··· + 0.993671a + 0.416563
a
12
=
u
u
a
4
=
−0.165445a
3
u
7
− 0.0257408a
2
u
7
+ ··· + 1.01296a − 0.199907
0.0490264a
3
u
7
+ 0.487530a
2
u
7
+ ··· + 1.00663a + 0.216656
a
6
=
−0.145990a
3
u
7
− 0.157999a
2
u
7
+ ··· + 0.226482a − 0.0429312
0.320279a
3
u
7
+ 0.344935a
2
u
7
+ ··· − 1.00696a − 0.581214
a
1
=
−0.223080a
3
u
7
− 0.106256a
2
u
7
+ ··· − 0.939315a + 0.0492462
0.243189a
3
u
7
+ 0.396678a
2
u
7
+ ··· − 2.17276a − 0.489037
a
5
=
−0.285211a
3
u
7
− 0.317493a
2
u
7
+ ··· − 0.363491a − 0.0576562
0.181058a
3
u
7
+ 0.185441a
2
u
7
+ ··· − 1.59693a − 0.595939
a
10
=
−u
u
3
+ u
a
2
=
−0.165445a
3
u
7
− 0.0257408a
2
u
7
+ ··· + 1.01296a − 0.199907
0.164961a
3
u
7
+ 0.644661a
2
u
7
+ ··· + 0.984109a + 0.398794
a
9
=
−0.310215a
3
u
7
− 0.191868a
2
u
7
+ ··· − 0.160858a − 0.210923
0.371570a
3
u
7
+ 0.332317a
2
u
7
+ ··· − 1.85032a − 0.481154
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
51112
282725
u
7
a
3
−
399104
282725
u
7
a
2
+ ··· −
27488
11309
a −
1177318
282725
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 7u
7
+ 17u
6
+ 14u
5
− u
4
+ 2u
3
+ 6u
2
− 4u + 1)
4
c
2
, c
8
u
32
− u
31
+ ··· − 18342u + 11689
c
3
, c
6
u
32
+ 7u
31
+ ··· − 32u + 7
c
4
, c
9
u
32
− u
31
+ ··· + 2638u + 469
c
5
, c
12
(u
2
− u + 1)
16
c
7
, c
10
, c
11
(u
8
− u
7
+ 5u
6
− 4u
5
+ 7u
4
− 4u
3
+ 2u
2
+ 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 15y
7
+ 91y
6
− 246y
5
+ 207y
4
+ 130y
3
+ 50y
2
− 4y + 1)
4
c
2
, c
8
y
32
+ 27y
31
+ ··· + 2039149884y + 136632721
c
3
, c
6
y
32
+ 3y
31
+ ··· − 548y + 49
c
4
, c
9
y
32
+ 35y
31
+ ··· − 3846760y + 219961
c
5
, c
12
(y
2
+ y + 1)
16
c
7
, c
10
, c
11
(y
8
+ 9y
7
+ 31y
6
+ 50y
5
+ 39y
4
+ 22y
3
+ 18y
2
+ 4y + 1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.647085 + 0.502738I
a = −0.608766 − 0.550255I
b = 0.182892 − 0.575506I
1.67479 − 0.15547I 1.58319 − 0.32355I
u = −0.647085 + 0.502738I
a = −0.804300 + 0.904540I
b = −0.766883 − 0.706358I
1.67479 − 4.21524I 1.58319 + 6.60465I
u = −0.647085 + 0.502738I
a = 0.575472 − 0.193692I
b = 0.785648 + 1.061200I
1.67479 − 4.21524I 1.58319 + 6.60465I
u = −0.647085 + 0.502738I
a = 0.1075680 − 0.0033399I
b = −0.499575 + 0.414336I
1.67479 − 0.15547I 1.58319 − 0.32355I
u = −0.647085 − 0.502738I
a = −0.608766 + 0.550255I
b = 0.182892 + 0.575506I
1.67479 + 0.15547I 1.58319 + 0.32355I
u = −0.647085 − 0.502738I
a = −0.804300 − 0.904540I
b = −0.766883 + 0.706358I
1.67479 + 4.21524I 1.58319 − 6.60465I
u = −0.647085 − 0.502738I
a = 0.575472 + 0.193692I
b = 0.785648 − 1.061200I
1.67479 + 4.21524I 1.58319 − 6.60465I
u = −0.647085 − 0.502738I
a = 0.1075680 + 0.0033399I
b = −0.499575 − 0.414336I
1.67479 + 0.15547I 1.58319 + 0.32355I
u = 0.283060 + 0.443755I
a = −0.741752 + 0.575430I
b = −0.28282 − 1.40078I
−4.93480 − 0.98388I −2.00000 − 3.22135I
u = 0.283060 + 0.443755I
a = 0.843131 + 0.210182I
b = 1.37494 + 1.03565I
−4.93480 + 3.07589I −2.00000 − 10.14955I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283060 + 0.443755I
a = 3.53954 + 0.62247I
b = 1.006860 − 0.355732I
−4.93480 − 0.98388I −2.00000 − 3.22135I
u = 0.283060 + 0.443755I
a = −3.27944 + 1.61382I
b = −0.215771 + 0.469647I
−4.93480 + 3.07589I −2.00000 − 10.14955I
u = 0.283060 − 0.443755I
a = −0.741752 − 0.575430I
b = −0.28282 + 1.40078I
−4.93480 + 0.98388I −2.00000 + 3.22135I
u = 0.283060 − 0.443755I
a = 0.843131 − 0.210182I
b = 1.37494 − 1.03565I
−4.93480 − 3.07589I −2.00000 + 10.14955I
u = 0.283060 − 0.443755I
a = 3.53954 − 0.62247I
b = 1.006860 + 0.355732I
−4.93480 + 0.98388I −2.00000 + 3.22135I
u = 0.283060 − 0.443755I
a = −3.27944 − 1.61382I
b = −0.215771 − 0.469647I
−4.93480 − 3.07589I −2.00000 + 10.14955I
u = 0.06382 + 1.51723I
a = −0.59184 − 1.50907I
b = −0.55330 − 2.21455I
−11.54440 + 0.15547I −5.58319 + 0.32355I
u = 0.06382 + 1.51723I
a = −1.44604 + 1.19889I
b = −0.332579 − 0.058640I
−11.54440 + 4.21524I −5.58319 − 6.60465I
u = 0.06382 + 1.51723I
a = 2.02681 + 1.39192I
b = 1.97903 + 1.60911I
−11.54440 + 4.21524I −5.58319 − 6.60465I
u = 0.06382 + 1.51723I
a = 2.54516 − 0.28930I
b = 1.072830 + 0.013443I
−11.54440 + 0.15547I −5.58319 + 0.32355I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06382 − 1.51723I
a = −0.59184 + 1.50907I
b = −0.55330 + 2.21455I
−11.54440 − 0.15547I −5.58319 − 0.32355I
u = 0.06382 − 1.51723I
a = −1.44604 − 1.19889I
b = −0.332579 + 0.058640I
−11.54440 − 4.21524I −5.58319 + 6.60465I
u = 0.06382 − 1.51723I
a = 2.02681 − 1.39192I
b = 1.97903 − 1.60911I
−11.54440 − 4.21524I −5.58319 + 6.60465I
u = 0.06382 − 1.51723I
a = 2.54516 + 0.28930I
b = 1.072830 − 0.013443I
−11.54440 − 0.15547I −5.58319 − 0.32355I
u = −0.19980 + 1.51366I
a = −1.337750 − 0.048574I
b = −1.080980 − 0.367558I
−4.93480 − 3.20880I −2.00000 − 0.42152I
u = −0.19980 + 1.51366I
a = 0.577550 − 0.281035I
b = 0.431533 + 0.452389I
−4.93480 − 3.20880I −2.00000 − 0.42152I
u = −0.19980 + 1.51366I
a = −1.71375 + 0.21126I
b = −0.977836 − 0.794944I
−4.93480 − 7.26857I −2.00000 + 6.50668I
u = −0.19980 + 1.51366I
a = 1.80840 + 0.61189I
b = 1.37603 + 1.31497I
−4.93480 − 7.26857I −2.00000 + 6.50668I
u = −0.19980 − 1.51366I
a = −1.337750 + 0.048574I
b = −1.080980 + 0.367558I
−4.93480 + 3.20880I −2.00000 + 0.42152I
u = −0.19980 − 1.51366I
a = 0.577550 + 0.281035I
b = 0.431533 − 0.452389I
−4.93480 + 3.20880I −2.00000 + 0.42152I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19980 − 1.51366I
a = −1.71375 − 0.21126I
b = −0.977836 + 0.794944I
−4.93480 + 7.26857I −2.00000 − 6.50668I
u = −0.19980 − 1.51366I
a = 1.80840 − 0.61189I
b = 1.37603 − 1.31497I
−4.93480 + 7.26857I −2.00000 − 6.50668I
14
III.
I
u
3
= h−u
12
−2u
11
+· · ·+b+2u, −u
12
−3u
11
+· · ·+a+2, u
15
+3u
14
+· · ·+u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
u
12
+ 3u
11
+ ··· − 6u − 2
u
12
+ 2u
11
+ ··· − 4u
2
− 2u
a
12
=
u
u
a
4
=
u
13
+ 3u
12
+ ··· − 6u − 2
u
13
+ 3u
12
+ ··· − 6u
2
− 2u
a
6
=
−u
12
− 3u
11
+ ··· − 6u − 1
−u
12
− 2u
11
+ ··· − 4u
2
− 2u
a
1
=
−u
14
− 4u
13
+ ··· + 6u + 1
−u
13
− 2u
12
+ ··· + u + 1
a
5
=
u
13
+ 3u
12
+ ··· − 6u − 2
u
13
+ 3u
12
+ ··· − 3u
2
− 2u
a
10
=
−u
u
3
+ u
a
2
=
u
14
+ 3u
13
+ ··· − 5u − 2
u
14
+ 3u
13
+ ··· − 6u
2
− 2u
a
9
=
−u
14
− 3u
13
+ ··· − 37u
2
− 9u
−u
9
− 3u
8
− 8u
7
− 15u
6
− 21u
5
− 24u
4
− 19u
3
− 10u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
14
+ 9u
13
+ 39u
12
+ 85u
11
+ 192u
10
+ 312u
9
+ 456u
8
+ 544u
7
+
524u
6
+ 425u
5
+ 230u
4
+ 94u
3
− u
2
− 5u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 13u
14
+ ··· + 135u − 13
c
2
, c
8
u
15
− u
14
+ ··· + 8u − 5
c
3
, c
6
u
15
+ u
13
+ ··· + 2u + 1
c
4
, c
9
u
15
+ 6u
13
+ ··· − 5u
2
+ 1
c
5
u
15
+ u
14
+ ··· + 4u + 5
c
7
u
15
+ 3u
14
+ ··· + u
2
+ 1
c
10
, c
11
u
15
− 3u
14
+ ··· − u
2
− 1
c
12
u
15
− u
14
+ ··· + 4u − 5
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 13y
14
+ ··· + 1221y − 169
c
2
, c
8
y
15
+ 13y
14
+ ··· + 134y − 25
c
3
, c
6
y
15
+ 2y
14
+ ··· + 14y
2
− 1
c
4
, c
9
y
15
+ 12y
14
+ ··· + 10y − 1
c
5
, c
12
y
15
+ 13y
14
+ ··· − 174y − 25
c
7
, c
10
, c
11
y
15
+ 17y
14
+ ··· − 2y − 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979786
a = 0.00878589
b = −0.425852
0.893453 −18.0630
u = −0.538899 + 0.815631I
a = −0.323491 − 0.663687I
b = 0.463057 − 0.615642I
2.80421 + 0.34444I 5.47559 − 1.58720I
u = −0.538899 − 0.815631I
a = −0.323491 + 0.663687I
b = 0.463057 + 0.615642I
2.80421 − 0.34444I 5.47559 + 1.58720I
u = −0.540426 + 0.399319I
a = 0.715731 − 0.927770I
b = 0.827811 + 0.993604I
3.92352 − 4.05135I 8.84525 + 7.48159I
u = −0.540426 − 0.399319I
a = 0.715731 + 0.927770I
b = 0.827811 − 0.993604I
3.92352 + 4.05135I 8.84525 − 7.48159I
u = 0.04766 + 1.49071I
a = −1.79550 − 0.47780I
b = −1.01433 − 1.13326I
−10.87770 + 3.02849I −1.19692 − 0.76371I
u = 0.04766 − 1.49071I
a = −1.79550 + 0.47780I
b = −1.01433 + 1.13326I
−10.87770 − 3.02849I −1.19692 + 0.76371I
u = 0.22132 + 1.48142I
a = 0.568013 + 0.587498I
b = 0.143716 + 0.621121I
−9.06968 − 0.10898I −0.251815 + 0.208478I
u = 0.22132 − 1.48142I
a = 0.568013 − 0.587498I
b = 0.143716 − 0.621121I
−9.06968 + 0.10898I −0.251815 − 0.208478I
u = −0.25430 + 1.48057I
a = −1.036910 − 0.006003I
b = −0.752315 − 0.563007I
−4.55807 − 4.26480I 1.35309 + 7.23493I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25430 − 1.48057I
a = −1.036910 + 0.006003I
b = −0.752315 + 0.563007I
−4.55807 + 4.26480I 1.35309 − 7.23493I
u = −0.15895 + 1.50654I
a = 1.85054 + 0.31350I
b = 1.16909 + 1.16141I
−2.43732 − 6.50952I 1.77219 + 6.05339I
u = −0.15895 − 1.50654I
a = 1.85054 − 0.31350I
b = 1.16909 − 1.16141I
−2.43732 + 6.50952I 1.77219 − 6.05339I
u = 0.213490 + 0.214314I
a = −3.98278 − 1.24606I
b = −0.624103 − 0.812395I
−4.90567 + 2.21151I −1.46603 − 0.60006I
u = 0.213490 − 0.214314I
a = −3.98278 + 1.24606I
b = −0.624103 + 0.812395I
−4.90567 − 2.21151I −1.46603 + 0.60006I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 7u
7
+ 17u
6
+ 14u
5
− u
4
+ 2u
3
+ 6u
2
− 4u + 1)
4
· (u
15
− 13u
14
+ ··· + 135u − 13)(u
25
− 18u
24
+ ··· + 200u − 192)
c
2
, c
8
(u
15
− u
14
+ ··· + 8u − 5)(u
25
+ u
24
+ ··· + 49u − 85)
· (u
32
− u
31
+ ··· − 18342u + 11689)
c
3
, c
6
(u
15
+ u
13
+ ··· + 2u + 1)(u
25
− 4u
23
+ ··· + 7u − 1)
· (u
32
+ 7u
31
+ ··· − 32u + 7)
c
4
, c
9
(u
15
+ 6u
13
+ ··· − 5u
2
+ 1)(u
25
+ 17u
23
+ ··· + u − 1)
· (u
32
− u
31
+ ··· + 2638u + 469)
c
5
((u
2
− u + 1)
16
)(u
15
+ u
14
+ ··· + 4u + 5)
· (u
25
+ 16u
24
+ ··· − 2816u − 256)
c
7
((u
8
− u
7
+ ··· + 2u
2
+ 1)
4
)(u
15
+ 3u
14
+ ··· + u
2
+ 1)
· (u
25
+ 8u
24
+ ··· − 42u − 4)
c
10
, c
11
((u
8
− u
7
+ ··· + 2u
2
+ 1)
4
)(u
15
− 3u
14
+ ··· − u
2
− 1)
· (u
25
+ 8u
24
+ ··· − 42u − 4)
c
12
((u
2
− u + 1)
16
)(u
15
− u
14
+ ··· + 4u − 5)
· (u
25
+ 16u
24
+ ··· − 2816u − 256)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 15y
7
+ 91y
6
− 246y
5
+ 207y
4
+ 130y
3
+ 50y
2
− 4y + 1)
4
· (y
15
− 13y
14
+ ··· + 1221y − 169)
· (y
25
− 28y
24
+ ··· + 395968y − 36864)
c
2
, c
8
(y
15
+ 13y
14
+ ··· + 134y − 25)(y
25
+ 23y
24
+ ··· − 26159y − 7225)
· (y
32
+ 27y
31
+ ··· + 2039149884y + 136632721)
c
3
, c
6
(y
15
+ 2y
14
+ ··· + 14y
2
− 1)(y
25
− 8y
24
+ ··· + 71y − 1)
· (y
32
+ 3y
31
+ ··· − 548y + 49)
c
4
, c
9
(y
15
+ 12y
14
+ ··· + 10y − 1)(y
25
+ 34y
24
+ ··· − 11y − 1)
· (y
32
+ 35y
31
+ ··· − 3846760y + 219961)
c
5
, c
12
((y
2
+ y + 1)
16
)(y
15
+ 13y
14
+ ··· − 174y − 25)
· (y
25
+ 14y
24
+ ··· + 393216y − 65536)
c
7
, c
10
, c
11
(y
8
+ 9y
7
+ 31y
6
+ 50y
5
+ 39y
4
+ 22y
3
+ 18y
2
+ 4y + 1)
4
· (y
15
+ 17y
14
+ ··· − 2y − 1)(y
25
+ 26y
24
+ ··· − 164y − 16)
21
